Question

using sound wave concepts to explain real - world scenarios
as elevation increases, temperature decreases. at which elevation will sound travel fastest?
elevation (meters) temperature of air (°c)
500 11.8
1,000 8.5
1,500 5.3
2,000 2.0
500 meters
1,000 meters
1,500 meters
2,000 meters

Explanation:

Step1: Recall sound - speed in air relation

The speed of sound in air is approximately given by the formula $v=\sqrt{\frac{\gamma RT}{M}}$, where $v$ is the speed of sound, $\gamma$ is the adiabatic constant, $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass of air. In general, the speed of sound in air increases with an increase in temperature.

Step2: Analyze given data

We are given that as elevation increases, temperature decreases. The temperatures at different elevations are: 500 meters - $11.8^{\circ}C$, 1000 meters - $8.5^{\circ}C$, 1500 meters - $5.3^{\circ}C$, 2000 meters - $2.0^{\circ}C$.

Step3: Determine the elevation with highest temperature

The highest temperature among the given data is $11.8^{\circ}C$ which occurs at an elevation of 500 meters. Since sound travels faster in warmer air, sound will travel fastest at the elevation with the highest temperature.

Answer:

500 meters